Question

2.
(11) Every real number is an
Are the square roots of all positive integers irrational? If not, give an example of the
square root of a number that is a rational number.
Show
can be represented on the number line.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

No. Square roots of all positive integers are not irrational. Example 4, 9, 16, etc. are positive integers and their square roots are 2, 9 and 4 which are rational numbers.

Let me give you one example : Show how √5 can be represented on the number line.  (The picture is in last )

Steps to show √5 on a number line.

Step: 1 – Draw a number line mm’

Step: 2 – Take OA equal to one inch, i.e. one unit.

Step: 3 – Draw a perpendicular AB equal to one inch (1 inch) on point A.

Step: 4 – Join OB. This OB will be equal to √2

Step: 5 – Draw a line BC perpendicular to OB on point B equal to OA i.e. one inch.

Step: 6 – Join OC. This OC will be equal to √3

Step: 7 – Draw a line CD equal to OA and perpendicular to OC.

Step: 8 – Join OD. This will be √4 i.e. equal to 2.

Step: 9 – Draw ED equal to 1 inch and perpendicular to OD.

Step: 10 – Join OE. This will be equal to √5

Step: 11 – Cut a line segment OF equal to OE on number line. This line segment OF will be equal to √5

See how, OE is equal to √5

Here, OD = 2, DE = 1 and angle ODE = 90º

Thus, according to Pythagoras theorem.

O E = √ O D 2 + D E 2

 

Or,  O E = √ 2 2 + 1 2

Or,  O E = √ 4 + 1

 

Or,  O E = √ 5